{
  "slug": "gear-ratio",
  "title": "Bike Gear Ratio Calculator",
  "category": "Cycling",
  "category_slug": "cycling",
  "tier": 2,
  "summary": "Calculate gear inches from chainring, rear cog, and wheel diameter to compare drivetrain ratios.",
  "description": "This calculator computes gear inches, a dimensionless measure of bicycle gearing, using the standard cycling mechanics formula: (chainring teeth ÷ rear cog teeth) × wheel diameter. It requires three inputs—chainring tooth count, rear cog tooth count, and wheel diameter in inches—and outputs the gear inches value, which represents the effective diameter of a directly driven wheel that would produce the same mechanical advantage. The gear ratio metric originated in the penny-farthing era and remains the standard method for comparing drivetrain configurations across different bicycles and wheelsets.",
  "page_url": "https://fitmetriclab.com/en/tools/cycling/gear-ratio/",
  "api_url": "https://fitmetriclab.com/api/tools/gear-ratio.json",
  "formula": {
    "id": "gear_ratio",
    "expression": "\\text{Gear inches} = \\frac{F}{R} \\times D",
    "variables": [
      {
        "symbol": "F",
        "description": "Front chainring teeth"
      },
      {
        "symbol": "R",
        "description": "Rear cog teeth"
      },
      {
        "symbol": "D",
        "description": "Wheel diameter in inches"
      }
    ]
  },
  "inputs": [
    {
      "id": "chainring",
      "label": "Chainring",
      "type": "number",
      "unit": "T",
      "default": 50,
      "min": 20,
      "max": 70,
      "step": 1
    },
    {
      "id": "cog",
      "label": "Rear Cog",
      "type": "number",
      "unit": "T",
      "default": 16,
      "min": 8,
      "max": 40,
      "step": 1
    },
    {
      "id": "wheel_diameter_in",
      "label": "Wheel Diameter",
      "type": "number",
      "unit": "in",
      "default": 27,
      "min": 20,
      "max": 32,
      "step": 0.1
    }
  ],
  "worked_example": {
    "inputs": {
      "chainring": 50,
      "cog": 16,
      "wheel_diameter_in": 27
    },
    "expected_output": "84.4\" gear inches"
  },
  "result_summary_template": "With a {chainring}-tooth chainring and {cog}-tooth rear cog on a {wheel_diameter_in}-inch wheel, the gear-inch calculation returns {result}.",
  "methodology": "Gear inches = (chainring teeth / rear cog teeth) × wheel diameter (inches). This formula, standardized in cycling mechanics literature, converts drivetrain gearing into an equivalent directly driven wheel diameter. The method originated in the penny-farthing era when wheel size directly determined gear ratio.",
  "sources": [
    {
      "label": "Wilson, D.G., Papadopoulos, J. Bicycling Science (3rd ed.). MIT Press. 2004.",
      "url": "https://mitpress.mit.edu/9780262731546/bicycling-science/"
    },
    {
      "label": "Brake, D., Stebbins, R.A. The Serious Leisure Perspective: An Introduction. Univ of Minnesota Press. 2007.",
      "url": "https://www.upress.umn.edu/book-division/books/the-serious-leisure-perspective"
    },
    {
      "label": "Sharp, A. Bicycles & Tricycles: A Classic Treatise on Their Design and Construction. Dover. 1896 (Reprint 1977).",
      "url": "https://store.doverpublications.com/0486238075.html"
    }
  ],
  "faqs": [
    {
      "question": "What are gear inches?",
      "answer": "Gear inches express the effective diameter of a directly driven wheel that would produce the same mechanical advantage as the actual drivetrain. A higher gear-inch value means a harder gear (more distance per pedal stroke), while a lower value indicates an easier gear. The measurement allows comparison across different wheel sizes and component combinations."
    },
    {
      "question": "How does wheel diameter affect the calculation?",
      "answer": "Wheel diameter scales the final gear-inch result proportionally. Larger wheels increase the gear-inch value for any given chainring-cog combination because each wheel rotation covers more ground. The calculator requires the nominal wheel diameter in inches; common road sizes include 27 inches (traditional) and 28 inches (700c), while mountain bikes typically use 26, 27.5, or 29 inches."
    },
    {
      "question": "Why does a smaller rear cog produce a higher gear?",
      "answer": "A smaller rear cog has fewer teeth, so the chain wraps around it fewer times per revolution. This increases the ratio of chainring teeth to cog teeth, causing the rear wheel to spin faster relative to pedal cadence. The result is a higher gear-inch value, meaning more resistance and greater distance traveled per pedal stroke."
    },
    {
      "question": "Can this calculator compare gearing across different bikes?",
      "answer": "Yes. Gear inches normalize comparisons by accounting for both drivetrain ratios and wheel size. A road bike with 50/16 gearing on 700c wheels can be directly compared to a mountain bike with 32/11 gearing on 29-inch wheels by calculating the gear inches for each setup. The tool does not account for tire width or actual rolling radius variations."
    },
    {
      "question": "What is the difference between gear inches and gear ratio?",
      "answer": "Gear ratio is the simple division of chainring teeth by rear cog teeth (e.g., 50 ÷ 16 = 3.125). Gear inches multiply this ratio by wheel diameter to produce a value that accounts for how far the bike travels per pedal revolution. Gear inches provide a more complete picture of mechanical advantage because they incorporate wheel size, while ratio alone does not."
    }
  ],
  "related_tools": [
    {
      "slug": "power-to-weight",
      "title": "Power-to-Weight Ratio Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/power-to-weight.json",
      "page_url": "https://fitmetriclab.com/en/tools/cycling/power-to-weight/"
    },
    {
      "slug": "chain-length",
      "title": "Chain Length Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/chain-length.json",
      "page_url": "https://fitmetriclab.com/en/tools/cycling/chain-length/"
    },
    {
      "slug": "climbing-watts",
      "title": "Climbing Watts Calculator",
      "api_url": "https://fitmetriclab.com/api/tools/climbing-watts.json",
      "page_url": "https://fitmetriclab.com/en/tools/cycling/climbing-watts/"
    }
  ],
  "last_updated": "2026-04-22",
  "price": {
    "value": 0,
    "currency": "USD"
  },
  "runs_in_browser": true,
  "disclaimer": "Educational estimate produced from a published formula. Not medical, nutritional, or training advice. Calculations are deterministic — apply the formula to the inputs to reproduce the result."
}